From: kovarik@mcmail.cis.McMaster.CA (Zdislav V. Kovarik)
Subject: Re: MATRICES TO IRRATIONAL POWERS
Date: 8 Feb 1999 01:27:46 -0500
Newsgroups: sci.math
Keywords: Basic matrix functions (exp, ln)

In article <smm22.1380.04F39E33@psu.edu>, theorist <smm22@psu.edu> wrote:
>Hi all,
>
>Can anyone please give me the name of a reference that will help me learn how 
>to treat matrices raised to irrational powers?  I have looked in several 
>mathematical physics texts and refs to no avial.
>
>reply here or email me if you can help!  Thanks a lot.
>
>cheer
>sue m.

Like with real or complex numbers: let A be a square matrix and t a
scalar, then

   A^t = exp(t*ln(A))

To find about exp, ln, and in general oter functions, there is a classic

F.R. Gantmakher: The Theory of Matrices, Vol. 1-2, Chelsea, New York 1959.

For practical implementations, see

Gene H. Golub and Charles F. Van Loan: Matrix Computations, 3rd Ed. (so
far), Johns Hopkins Univ. Press, Baltimore 1996.

Good luck, ZVK(Slavek).